APPENDIX B Worked example – Design of a truss node with gusset
2. Gusset plate to web chord welded
This connection is a welded plate perpendicular to the web of the chord, see Figure B.6. The two fillet welds are identical. The design of the gusset plate and its weld to the chord takes into account the axial forces in all three angle members connected to it.
O
α3 α1
Y Z
260 320
30 260
Og
N1,Ed N2,Ed
N3,Ed
Figure B.6 Gusset plate to web chord welded connection
The longitudinal axes of all three angle members intersect on the chord axis at the point O in the web.
The gusset plane is not positioned symmetrically about the normal OY to the web plane (see Figure B.6 and Figure B.7). The moment resulting from the eccentricity eZ should be taken into account.
The moment resulting from the eccentricity eY = tw/2 can be neglected.
Y
Z O
eZ=30
eY=7,5/2 Og
Y
X O
Og
tw=7,5
tg=15
Figure B.7 Gusset plate to web chord – Details
The basic assumption is that gusset plate transfers axial forces acting in its plane and in the direction of the member axes.
2.1. Data
Global coordinates system (see Figure B.6 and Figure B.7) The YOZ Plane is that of the gusset plate
The XOZ Plane is that of the chord web Geometric data
Gusset plate thickness tg = 15 mm Web thickness tw = 7,5 mm Angle between gusset and web a = 90°
Number of fillet welds na = 2
Effective throat thickness a = Value to be defined Length of welds Lw = 560 mm
Material data
Partial Factor
Resistance of weld: M2 = 1,25 (recommended value) EN 1993-1-8 Table 2.1 NOTE Internal forces in the truss members (see Figure B.6)
All axial forces are applied in the gusset plate XOZ plane:
Tension axial force at an angle to normal OY of 1 = 42°:
N1,Ed = 406,9 kN
Tension axial force on the normal OY so 2 = 0°
N2,Ed = 2,6 kN
Compression axial force at an angle to normal OY of 3 = -41,3°
N3,Ed = -609,4 kN
2.2. Stresses in the gusset cross-section in front of welds
The approach is based on a linear-elastic analysis that leads to a safe estimation of the resistance of the welded joint.
EN 1993-1-8 2.4(2)
2.2.1. Design forces in the gusset plate at the chord web face The effects of the small eccentricity eY from the chord axis will be neglected.
The gusset plate section is verified for the following forces:
Ng,Ed Axial force at an eccentricity of eZ = 30 mm to the centreline of the gusset plate
Vg,Ed shear force
With:
3
1 i
i i
Ed
g, N cos( )
N
3
1 i
i i
Ed
g, N sin( )
V
and Mg,Ed, the moment resulting from the eccentricity, Mg,Ed eZ Ng,Ed Then: Ng,Ed = -152,83 kN
Vg,Ed = 674,47 kN Mg,Ed = 4,585 kNm
Note: the high axial force component Ng,Ed is due to the local point load at the joint and the self weight of the truss.
2.2.2. Normal stress
Assuming a uniform distribution of the load in the section, the normal stress is:
v I M A
N
g Ed g, g
Ed g, max
g,
Where: Ag is the cross-section area
Ig is the second moment of cross-section v is the position of the end fibre
With: 580Ag tg Lw 15 = 8700 mm2
12
3w g g
L
I t = 243,89.106 mm4 v = 290 mm
Then: g,max= -23,02 N/mm2 2.2.3. Shear stress The shear mean stress is:
g Ed g,
g A
V
Then: g= 77,53 N/mm2
One usually checks the combination of axial and shear stresses in the gusset plate section using the Von Mises criterion.
2.3. Design resistance of the fillet weld
The design resistance of a fillet weld should be determined using either the directional method or the simplified method.
EN 1993-1-8 4.5.3.1(1) The directional method is based on the comparison between the design tensile
strength and the applied stress in the most severely loaded part of the weld throat. The applied stress, being determined from a Von Mises formulation, accounts for the influence on the weld strength of the inclination of the resultant force per unit length to the weld axis and plane.
The simplified method is based on the design shear strength of the weld to which is compared directly to an applied weld throat shear stress obtained by dividing the resultant force per unit of length b the weld throat size. The simplified method is always safe compared to the directional method.
Here, the directional method is applied. EN 1993-1-8
4.5.3.2 2.3.1. Directional method
Note: the normal stress in the weld needs not to be considered. EN 1993-1-8 4.5.3.2(5) On the throat section of the weld, the force per unit length are:
a = sin( a /2)
a g max
g,
n
e = -122,08 N/mm.mm
a = cos( a /2)
a g max
g,
n
e = -122,08 N/mm.mm
a =
a g g
n
e
= 581,44 N/mm.mm
The design resistance of the fillet weld will be sufficient if the following conditions are both fulfilled:
w = [2+3 (2+2) ]0,5 ≤ fu / (wM2)
≤ 0,9 fu / M2
EN 1993-1-8 4.5.3.2(6)
Where: w is the correlation factor for fillet weld
w = 0,8
EN 1993-1-8 Table 4.1
These conditions can be rewritten in the following forms:
(a w) / a ≤ fu / (wM2) (a ) / a ≤ 0,9 fu / M2
From these conditions, a minimum value for the effective throat thickness is derived.
a1,min = a w / [ fu / (wM2)] = 2,03 mm a2,min = a / (0,9 .fu / M2) = 0,33 mm amin = max(a1,min ; a2,min) = 2,03 mm The following requirements must be satisfied:
a 3 mm
leff max(30 mm ; 6 a) with leff = Lw – 2 a
EN 1993-1-8 4.5.2(2) 4.5.2(1) An effective throat thickness of 4 mm is then sufficient.